Symmetry and Balanced Designs

Overview

In this second lesson of Maths Across Aotearoa, learners explore symmetry as a precise mathematical idea: two sides match when a shape or design is folded along a line. They build on prior work recognising and describing 2D shapes, using folding, mirrors, movement and geoboards to identify and create lines of symmetry.

Learning intentions

• WALT explain what a line of symmetry is.
• WALT identify lines of symmetry in familiar 2D shapes and designs.
• WALT create balanced designs using folding, mirrors and geoboards.
• WALT explain how we know that both sides match.

Success criteria

• I can draw a line of symmetry on a square.
• I can find symmetry in two different shapes.
• I can test symmetry by folding or using a mirror.
• I can create a shape with more than one line of symmetry.

Curriculum links

• Mathematics and Statistics — Mathsteasers: higher-order thinking questions that challenge advanced learners and deepen understanding.
• Mathematics and Statistics — Mathsteasers / Alignment: mathematical challenge connected to familiar shape and geometry learning.
• Mathematical practices: noticing and describing patterns, using representations, testing ideas, and explaining reasoning.
• Learner competencies: thinking critically, using language and symbols, and participating positively in collaborative problem-solving.

Lesson structure (60 minutes)

1. 0–7 min · Hook and movement. Teacher displays the symmetry hook and learning intention slides and shows two designs: one attractive but not symmetrical, and one symmetrical. Ask, “Does looking balanced always mean a design is symmetrical?” Students make a body shape with a partner, copy each other, and share an initial idea about symmetry.

2. 7–17 min · Direct teaching and modelling. Teacher uses the symmetry teaching slides to define a line of symmetry as a line where both sides match exactly when folded; model folding a paper square and test possible lines with a mirror. Emphasise that symmetry is not simply about a design looking attractive. Students predict, test and discuss which lines work, then observe that a square has four possible lines of symmetry and an equilateral triangle has three.

3. 17–27 min · Guided shape investigation. Teacher gives each pair a small set of paper 2D shapes and mirrors, referring to the shape investigation instructions; demonstrate placing the mirror on a possible line and checking whether the reflected half completes the shape. Students work in pairs to find and mark lines of symmetry, recording whether each shape has none, one, or more than one line.

4. 27–42 min · Symmetry hunt. Teacher distributes the symmetry hunt and recording sheet and leads a visual, tactile and language-supported hunt around the classroom. Students inspect familiar designs, objects and classroom features, using folding where possible and a mirror where folding is not practical; they sketch two examples, mark the line or lines, and complete the sentence, “I know this is symmetrical because…”

5. 42–54 min · Geoboard design challenge. Teacher shows the geoboard challenge and discussion prompts and models making one half of a design before reflecting it across a vertical or horizontal line. Students use geoboards and bands to complete the Must Do: draw a line of symmetry on a square; Can Do: find symmetry in two shapes; Try: create a shape with more than one line of symmetry. Partners test each design by folding a drawn copy or placing a mirror along the line.

6. 54–60 min · Share and exit check. Teacher invites two or three pairs to display a design and explain how they tested it, then returns to the plenary and exit-question slide. Students complete the final boxes on the symmetry hunt and recording sheet: draw one line of symmetry on a square and write one sentence explaining why it works.

Resources

• the symmetry hook and learning intention slides
• the symmetry teaching slides
• the shape investigation instructions
• the geoboard challenge and discussion prompts
• the plenary and exit-question slide
• the symmetry hunt and recording sheet
• Paper squares and assorted paper 2D shapes
• Small mirrors, pencils and coloured pencils
• Geoboards and elastic bands
• Classroom objects or photographs of familiar designs

Assessment

• Listen for learners distinguishing “looks balanced” from “matches when folded”; ask, “How could you prove it?”
• During the hunt and geoboard task, check whether learners draw the line on the fold/reflection boundary rather than through an arbitrary attractive part of the design.
• Use the exit response to identify who can draw a valid line of symmetry on a square and justify it. Revisit misconceptions in the next lesson.

Differentiation

• Support learners with pre-drawn possible lines, paper shapes that can be folded, larger mirrors, a partner role such as “tester” or “explainer”, and sentence starters: “The line of symmetry is…”, “Both sides match because…”.
• Provide visual demonstrations, repeated oral instructions, gesture and movement, and opportunities to handle shapes for learners needing tactile or language support, including EAL learners.
• Challenge confident learners to create a design with two, three or more lines of symmetry, compare designs, and explain why a shape cannot have a chosen line.
• For learners with fine-motor or visual needs, provide larger shapes, high-contrast outlines, pre-stretched bands and the option to explain orally or use a mirror instead of drawing every line.